Existence of positive solution for a class of quasilinear Schrödinger equations with potential vanishing at infinity on nonreflexive Orlicz-Sobolev spaces

In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive - _ u +V (x) (|u|) u= K (x) f (u) R^N, where N 2, V, K are nonnegative continuous functions and f is a continuous function with a quasicritical growth. Here we extend the Hardy-type inequalities presented in AlvesandMarco to nonreflexive Orlicz spaces. Through inequalities together with a variational method for non-differentiable functionals we will obtain a ground state solution. We analyze also the problem with V=0.